Question

simplify by rationalizing the denominator 5 / root 7 - root 5​

Answer 1

Solution!!

5/(√7 - √5)

Rationalising the denominator.

= 5/(√7 - √5) × (√7 + √5)/(√7 + √5)

= 5(√7 + √5)/(√7 - √5)(√7 + √5)

Use (a - b)(a + b) = a² - b² to simplify.

= 5(√7 + √5)/((√7)² - (√5)²)

= 5(√7 + √5)/(7 - 5)

= 5(√7 + √5)/(2)

Distribute 5 through the parentheses in the numerator.

= (5√7 + 5√5)/2

More information:-

In brief, rationalising the denominator means to simplify the denominator in such a way that it no longer has any surds. It becomes a rational number. This is done to make it easy for us to understand what the quantity really is.